This invention relates to the technology of charged particle lithography and, more particularly, relates to a charged particle beam writing method and writing system to reduce a proximity effect.
In recent years, electron beam writing system have popularly been used for drawing fine patterns on samples such as semiconductor wafers and mask substrates. However, such apparatus are accompanied by a problem of distorted patterns given rise to by back scattering electrons, which is called as proximity effect.
The exposure dose correction method is an effective way of correcting the proximity effect. With this method, the exposure dose by electron beams is defined for each position to be exposed to electron beams on the sample as a function of the size of drawing pattern and the line density of the pattern to be drawn. Known techniques for defining the exposure dose include (a) the one using a matrix (M. Parikh, J. App. Phys. 19, p4371, p4378, p4383 (1979)) and (b) the one using simple approximation formulas (e.g., J. M. Parkovich, Journal of Vacuum Science & Technology B4, p159 (1986)).
With technique (a), the relationship between the exposure dose and the exposure dose is expressed in terms of a matrix for each position to be exposed to electron beams on the sample and an optimal exposure dose is obtained for the position by determining an inverse matrix for the given matrix. This technique is advantageous in that the determined optimal exposure dose is accurate if a sufficiently small figure is used for determining the exposure dose. On the other hand, it has a disadvantage of consuming enormous time for various calculations. For instance, several hundred to several thousand hours may be required to correct the exposure dose for an entire LSI chip for direct drawing.
With technique (b), an approximate optimal exposure dose D,is determined by calculation using, for example, the following formulas. EQU D'=C/(1/2+.eta.U) (i) EQU U=(1/.pi.).intg. exp {-(x-x').sup.2 }dx' (ii)
where C is a constant and .eta. is the ratio of the exposure dose of the applied resist to forward scattering electron beams to the exposure dose of the resist to back scattering electron beams. The integral of parameter U is determined for the area to be patterned.
(In the following description, the size, length and position of the figure are normalized so as to make the amplitude of back scattering .sigma..sub.b equal to 1.)
It will be understood by referring to FIG. 1 that equation (ii) can be transformed into formula (iii) below. EQU U=.SIGMA.{erf(x.sub.Ri -x)-erf(x.sub.Li -x)}.times.{erf(y.sub.Ui -y)-erf(y.sub.Di -y)} (iii)
where erf represents an error function and the integration range is between 0 and u. EQU erf=.pi..sup.-1/2 .intg. exp (-u.sup.2)du (iV)
Thus, the exposure dose is estimated at position (x, y) and the addition using .SIGMA. is conducted for rectangles located, at least partly, within a circle having its center at (x, y) and a radius of about 2 to 3. The circle may be replaced by a square or a rectangle having its center also at (x, y) and sides that are about 4 to 6 long.
Calculations using formulas (iii) and (iv) can be carried out very quickly if the following procedures are employed.
(I) Prepare in advance a table for the error function. PA0 (II) Determine the value of parameter U for each peripheral figure, using the table of (I) and carrying out the calculation of formula (iii). PA0 (III) Determine an approximate optimal exposure dose, using the result of (II) and formula (i).
As will be seen from above, the technique of using approximation can be operated very quickly. In fact, the operation of correcting the LSI pattern directly drawn by electron beams can be carried out in an hour for a chip by also using the representative figure method. Note however, the obtained result represents an approximate value after all.
FIGS. 2A and 2B illustrate the error that occurs with the approximation technique. FIG. 2B shows the absorbed energy amount in a resist observed along the dotted chain line of FIG. 2A when a pattern as shown in FIG. 2A is irradiated with electron beams. In FIG. 2B, the solid line shows the ideal exposure dose, whereas the broken line shows the approximate exposure dose obtained by formula (i).
As shown in FIGS. 2A and 2B, the error in the exposure dose can be as large as 3 to 4%, which has been neglected but is not negligible when lines with a minimal width of less than 0.2 .mu.m are drawn directly by electron beams. In the case of preparing a reticle, the lines on the reticle may show a width that is as small as less than 0.5 .mu.m.
Calculations for proximity effect correction are performed for the entire area of the pattern to be formed by lithography to consequently give rise to a problem as described below if calculations are carried out for proximity effect correction within the electron beam writing system. For instance, if the calculations for proximity effect correction takes an hour and the lithographic operation also takes an hour, the time consumed for the entire operation including the operation of proximity effect correction will be two hours.
A huge amount of data is required for drawing a large LSI pattern and a high precision level is required for drawing an LSI pattern with an enhanced degree of integration. As a result, the time required for the calculations involved in the operation of proximity effect correction will become enormous than ever. If the time consumed for the calculations using hardware is held to a realistic level, the electron beam writing system cannot carry out a pattern drawing operation without a large set of figure data necessary for drawing a pattern. Thus, the time required for the calculations can significantly reduce the operating efficiency of the electron beam writing system. In some cases, the operation of proximity effect correction can take a large part of the operating hours of an electron beam writing system.
In short, known techniques of correcting the proximity effect by correcting the exposure dose are accompanied by the following problems. Firstly, while those involving the use of a matrix may be precise, they can consume a large amount of time for calculations. Secondly, accuracy is sacrificed if approximation is used for the calculations in order to reduce the time consumption. Thirdly, the time consumed for proximity effect correction increases with the increase in the size of the pattern to be drawn and the rise of the required precision level to consequently reduce the operating efficiency of the charged particle writing system.